Probably too late now for the guy above but
https://equiniti.com/uk/legal-notice/
Equiniti are regulated by the FCA. (it's in the link above as is their commitment to the Plain English campaign lol)
FCA principles for business, Principle 7 "Communications"
A firm must pay due regard to the information needs of its clients, and communicate information to them in a way which is clear, fair and not misleading.
I 100% guarantee that a formal recorded letter to their customer complaints department (or head office if you can't find the address) stating that unless they buck up you will complain to the FCA, will get their attention.
Edit
Interestingly, after some searching, I could not find a clear, identifiable complaints procedure. I'm almost looking forward to them screwing up with me sometime now. Nothing like going all Victor Meldrew on their arses when you have the inside track!
PS
Just in case anybody is interested...a complaint to the FCA will lead to an admin charge of +£500 to the firm concerned...
irrespective of the outcome of the complaint!! Regulated firms get a small handful of freebies per year. For a company the size of Equiniti you can pretty much guarantee they will all be used up by about the 5th of January
.